Equation 17 · The Statistical Mechanics of Irreversibility at Molecular Scale
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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol d
d is part of the quantity the equation computes from the expression on the right.
Symbol U
U is part of the quantity the equation computes from the expression on the right.
Symbol delta
delta is one of the signed contributions combined to compute the quantity on the left.
Symbol W
W is one of the signed contributions combined to compute the quantity on the left.
Symbol Q
Q is one of the signed contributions combined to compute the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
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What the article says around this equation
For an overdamped particle in a potential U(x,) , an infinitesimal energy balance can be written schematically as . with work associated with changing the control parameter and heat associated with motion through the force field. The distinction depends on the physical protocol, not merely on algebraic rearrangement. Stochastic energetics must also specify a calculus convention when multiplicative noise is present.
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